Constantly appear "little disk space"
most likely, a speech about the lack of free space in the file system. You can delete “extra” packages and “extra” files in your home directory ( /home/имя-пользователя ).
I wanted to install Ubuntu 14.04LTS, but I can’t get it because of "not enough disk space".
and here, most likely, we are talking about the absence of unallocated disk space.
You can (directly in the installer) delete, for example, those partitions that are currently used by ubuntu 12.04 . there should be at least two of them - the root partition (with all these files and directories, what you see on the photo you attached) and the swap partition ( swap ) and continue the installation — the installer will find the free space itself.
Attention! - while all your saved files / directories "disappear", and those that you really need, it makes sense to save to some other media.